物理学报Issue(5)：9-15,7.DOI:10.7498/aps.64.050301
相空间中对应量子力学基本对易关系的积分变换及求Wigner函数的新途径∗
An integral-transformation corresp onding to quantum mechanical fundamental commutative relation and its application in deriving Wigner function
摘要
Abstract
In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1π ::exp[±2i (q−Q) (p−P )]::, here ::::denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules(P−Q ordering, Q−P ordering and Weyl ordering). We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained. In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1π ::exp[±2i (q−Q) (p−P )]::, here ::::denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules(P−Q ordering, Q−P ordering and Weyl ordering). We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained.关键词
对易关系/积分变换/Weyl编序/Wigner函数Key words
commutative relation/integral transformation/Weyl ordering/Wigner function引用本文复制引用
范洪义,梁祖峰..相空间中对应量子力学基本对易关系的积分变换及求Wigner函数的新途径∗[J].物理学报,2015,(5):9-15,7.基金项目
国家自然科学基金(批准号:11175113,11275123)资助的课题.@@@@* Project supported by the National Natural Science Foundation of China (Grant Nos.11175113,11275123) （批准号:11175113,11275123）
